The case stems from a complaint by Brazilian group DIS, the former owner of a percentage of the player's rights.
Barcelona officially said the transfer cost 57.1 million euros ($63.6 million), with 40 million euros going to Neymar's family and 17.1 million to Santos, but Spanish prosecutors later said it actually cost at least 83.3 million euros.
All the defendants have denied any wrongdoing, but appeals by them to Spain's high court have been rejected, forcing the case to go to trial.
DIS, which received 6.8 million of the 17.1 million euros paid to Santos, has alleged that Barca and Neymar joined forces to hide the real amount of the transfer.
On Wednesday, DIS said it was "satisfied" that there is now a date for the trial of the case, which has been in the Spanish courts since 2016.
The prosecution has requested a two-year prison sentence for Neymar, but he has insisted he was only focused on football and that he blindly trusted his father, who is also his agent.
Bartomeu took over the Barcelona presidency from his good friend Rosell, after the latter resigned in January 2014 as he faced charges of corruption over the transfer.
In 2020, Barcelona said they had been cleared by the Court of Arbitration for Sport over claims of fraud.
A document in 2020 showed Neymar owed more unpaid tax than any other individual on a Spanish authorities' blacklist.
The tax office refused to say whether Neymar's presence on that list was linked to his transfer from Santos.
'Tax planning error'
Barcelona agreed to pay a fine of 5.5 million euros to avoid a trial in 2016 over alleged tax fraud in the signing of Neymar.
Then-president Bartomeu said at the time there had been a "tax planning error".
Neymar has also been in trouble with Brazilian tax authorities, being fined for tax evasion in Brazil.
The 30-year-old has recently been playing on PSG's pre-season tour of Japan as they build up for the season-opening French Champions' Trophy against Nantes on Sunday in Tel-Aviv.
He signed an extension to his contract with the French side last year, taking him up to 2025.
However, another disappointing season blighted by injury has placed question marks over his future at the Qatari-owned club.
Neymar said Saturday that he wants to stay with the French side and does not "need to prove" himself after five years with PSG.
The player, Brazil's second highest goal-scorer of all time behind Pele, will be hoping to lead his country to a record-extending sixth World Cup title in Qatar.
Brazil's World Cup campaign gets under way with a group match against Serbia on 24 November, three days after the start of the tournament.